Ergodic Interference Alignment with Noisy Channel State Information

We investigate the time-varying Gaussian interference channel (IC) in which each source desires to communicate to an intended destination. For the ergodic time-varying IC with global perfect CSI at all terminals, it has been known that with an interference alignment technique each source-destination pair can communicate at half of the interference-free achievable rate. In practice, the channel gains are estimated by transmitting known pilot symbols from the sources, and the channel estimation procedure is hence prone to errors. In this paper, we model the channel estimation error at the destinations by an independent additive Gaussian noise and study the behavior of the ergodic interference alignment scheme with the global noisy CSI at all terminals. Toward this end, we present a closed-form inner bound on the achievable rate region by which we conclude that the achievable degrees of freedom with global perfect CSI can be preserved, if the variance of channel estimation error is proportional to the inverse of the transmitted power.